Finite Group Databasebeta

← #32973858

Subgroups — #32973858

Order 18688.

138 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 138 conjugacy classes of subgroups — too many to draw. Only its 25 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22609530C211yesmaximal, characteristic
2#22608098C211yesmaximal, characteristic
3C73×#1409C211yesmaximal, characteristic
4#17988985C411yescharacteristic, complemented
5#17988939—21no—
6#17988933—21no—
7#17988386—21no—
8C8×#10596831C411yescharacteristic, complemented
9#492×C73C2211yescharacteristic
10#353×C73—21no—
11#14556591—21no—
12#14556523—41no—
13#14556514—42no—
14#14556512—42no—
15#14556510—41no—
16C4×#10596831—21no—
17C2×SD16×C73—41no—
18C4⋊Q8×C73D411yescharacteristic
19#127×C73D411yescharacteristic
20#99×C73—41no—
21C4×C8×C73C2×C411yescharacteristic
22C2×Dic146—41no—
23#11924012—81no—
24C2×#10596831—22no—
25C4⋊Dic73—41no—
26C4⋊Dic73—41no—
27C2×Q8×C73—21no—
28C2×D4×C73—21no—
29C2×D4×C73—41no—
30SD16×C73—82no—
31C2×C8×C73—21no—
32C4⋊C4×C73—41no—
33C22⋊C4×C73—81no—
34C42×C73C22⋊C411yescharacteristic
35C23×C73—41no—
36Q8×C73—81no—
37D4×C73—81no—
38D4×C73—82no—
39C2×C4×C73—21no—
40C2×C4×C73—41no—
41C2×C4×C73—161no—
42C2×C4×C73#9911yescharacteristic
43C2×Dic73—81no—
44Dic146—82no—
45C8×C73—22no—
46#10596831—42no—
47#10596831—161no—
48C22×C73—81no—
49C22×C73—161no—
50C22×C73#35311yescharacteristic
51C4×C73—22no—
52C4×C73—21no—
53C4×C73—81no—
54C4×C73—321no—
55Dic73—161no—
56#7536—731nomaximal, Sylow
57C2×C73—21no—
58C2×C73—161no—
59C2×C73#140911yescharacteristic
60#1708—731no—
61#1410—731no—
62#1409D7311yescharacteristic
63C73#753611yescharacteristic, complemented, Sylow
64#498—731no—
65#492C2×D7311yescharacteristic
66#487—1461no—
67#486—1461no—
68#356—1461no—
69#353—21no—
70C82—731no—
71C2×SD16—41no—
72C4⋊Q8—1461no—
73C4⋊Q8D29211yescharacteristic
74#127C22⋊D7311yescharacteristic
75#106—2921no—
76#103—2922no—
77#102—2922no—
78#101—2921no—
79#99—41no—
80C4×C8—1461no—
81C4×C8C4×D7311yescharacteristic
82C2×Q8—21no—
83C2×Q8—2921no—
84C2×D4—21no—
85C2×D4—41no—
86SD16—82no—
87M16—5841no—
88C2×C8—21no—
89C2×C8—1462no—
90C4⋊C4—41no—
91C4⋊C4—2921no—
92C4⋊C4—2921no—
93C22⋊C4—81no—
94C42#1192400511yescharacteristic
95C23—41no—
96Q8—81no—
97Q8—5842no—
98D4—81no—
99D4—82no—
100C2×C4—21no—
101C2×C4—41no—
102C2×C4—161no—
103C2×C4—5841no—
104C2×C4#1455650511yescharacteristic
105C8—22no—
106C8—2922no—
107C8—11681no—
108C22—81no—
109C22—161no—
110C22#1798837911yescharacteristic
111C4—22no—
112C4—21no—
113C4—81no—
114C4—321no—
115C4—11681no—
116C2—21no—
117C2—161no—
118C2#2260809511yescharacteristic
subgroupG/H
centerC2#22608095
commutatorC4×C8×C73C2×C4
Frattini#492C2×D73
FittingC73×#1409C2
socleC2×C73#1409
prime radical#127×C73D4
cosocle#492×C73C22
hypercenter#1409D73
hypocenterC73#7536
LCSG ▷ C4×C8×C73 ▷ C42×C73 ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #492 ◁ #1409

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. #17988985C4semidirect
8. C8×#10596831C4semidirect
63. C73#7536semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#226095302
#226080982
C73×#14092
#753673